Clutchness in Basketball

Home , Dwight Howard, Shot clock, Steve Nash

CLUTCHNESS IN BASKETBALL

A Project

Presented to the

Faculty of

California State Polytechnic University, Pomona

In Partial Fulfllment

Of the Requirements for the Degree

Master of Science

Economics

Arvin Barkazian

2019 SIGNATURE PAGE

PROJECT: CLUTCHNESS IN BASKETBALL

AUTHOR: Arvin Barkazian

DATE SUBMITTED: Spring 2019

Department of Economics

Dr. Craig Kerr Project Committee Chair Economics

Dr. Carsten Lange Economics

Dr. Greg W. Hunter Economics

ii ACKNOWLEDGMENTS

Thank you Dr.Kerr, Mom and Dad for all your support and technical input. Thank you

Michelle, for everything.

iii ABSTRACT

The purpose of this project is to explore the concept of clutchness in basketball. More specifcally, this project focuses on late game free throw shooting in close games during the playoffs and the effect point differential has on free throw shooting. Twenty NBA players over the past 20 years are studied to determine if point differential (how close the game is) effect free throw shooting in a signifcant way. Furthermore, if point differential is signifcant, a ranking of these players will be created from most clutch to least clutch.

iv Contents

Signature Page ii

Acknowledgments page iii

Abstract iv

1 Introduction 1

1.1 Clutch Situation ...... 2

1.2 Basketball ...... 2

1.3 Literature ...... 3

2 Data 6

2.1 Point Differential and Other Independent Variables ...... 7

3 Methodology 9

3.1 Models ...... 10

3.2 Player Ranking ...... 10

4 Results 12

4.1 Limiting Data To Elimination Games ...... 14

4.2 Free Throw Attempts and Shortcomings of Data ...... 14

v 4.3 Player Ranking ...... 16

5 Conclusion 19

Bibiliography 21

vi Chapter 1

Introduction

An argument about clutchness in sports is commonplace at any local bar. Fans love to boast that no matter what the numbers say, when it counts, their favorite players score the winning basket. This mentality does not terminate with fandom, players and broadcasters have created nicknames for players whom they believe are “clutch”. A great example of this is Damion Lilard of the Portland Trailblazers who has earned himself the nickname

“Dame Time” for his alleged late game heroics (Young, 2019). And of course, Kobe

Bryant, whom they called “The Black Mamba” (Rovell, 2016). But is there any truth to this? Many of these clutch players earn their reputation in spectacular performances during a few games over their career and all evidence of their clutchness seems to inevitably to point to these few instances of greatness. On May 2nd, 2014 Damian Lillard ended the playoff run of the Houston Rockets by scoring a long 3 point attempt as the shot clock expired.

1 1.1 Clutch Situation

If one asks a sports fan what does it mean to be “clutch”, the answers will likely vary widely with no real mathematical defnition. Clutch moments are generally thought of as moments where “the game is on the line” and every point is critical. The National

Basketball Association provides a more formal defnition of clutch moments. In the

NBA, a moment is defned to be clutch if there is less then 5 minutes left in the game and the point differential is 5 or less (Beuoy, 2014). This is simply a close game that is about to end. This paper will restrict this defnition even further by adding the requirement that the game must be in the playoffs. During the regular season, it is common knowledge that many teams will miss important shots and free throws on purpose in order to lose games and improve their odds of landing a higher draft pick (Price et al., 2010). Furthermore, good teams in the second half of the seasons will sometimes be so far ahead of others in the standings that a clutch situation, even if the game is close and about to end, provides no real pressure (the pressure of possibly loosing an important game). This pressure is, of course, what may cause players to perform differently and the reaction to this pressure is what this paper aims to capture. Simply put, the regular season is too long and too unimportant for there to be reliable clutch moments. For this paper, a clutch situation will be during the playoffs with 5 minutes left in the game and will be focusing on free throw shooting.

1.2 Basketball

There are two ways to score in basketball, free throws and feld goals. Field goals con- tribute the most points as they are scoring that happens in the natural fow of the game.

There are two types of feld goals, three pointers which are worth three points and two

2 pointers which, of course, are worth two. The second way to score is the type this paper will focus on, free throws. Free throws do not happen in the natural fow of the game. A player receives free throws when he is fouled while attempting a feld goal. The number of free throws is determined by the type of feld goal that was being attempted. If a three pointer was being attempted, three free throws are awarded and two for two pointers.

A natural question one might ask is: If feld goals are the main way to score in basketball, why focus on free throws for this project? In the clutch, defenses in every team sport have been known to pick up the intensity. There are many examples of teams who have won championships by tough late game defense. The 1989 and 1990 Detroit Pistons famously won two championships with this strategy, earning themselves the nickname

“The Bad Boys”. This, of course, effects their opponents feld goal percentage and makes it more diffcult to discern whether the players in questions are clutch (or chokers) or are simply being held back by much more intense defense. To circumnavigate this issues, this paper turns to free throws. No defense is played during free throws, the clock is stopped, and the player is asked to perform a task that he/she has practiced thousands of times. Free throws isolate the players and the task at hand. Much like a game of golf, the only thing the player must do is put the ball in the hole.

1.3 Literature

An investigation of clutch free throw shooting is, in truth, a psychological question.

As point differential shrinks, pressure increases, nothing else about free throw shooting changes in a hotly contested game. Otten (2009) investigates this by conducting a unique free throw shooting experiment on random individuals. The authors create two scenarios, one to simulate a non-pressure environment and one to create a pressure environment.

3 Fifteen free throws are taken in both scenarios, in the pressure scenario, the shooters

were taped by a camera to create the pressure. The authors fnd that “Results of the

model suggest that reinvesting attention in the task leads to greater anxiety (cognitive and

somatic), which then predicts a higher level of self-focus; self-focus, then, did not lead

to improved performance under pressure, whereas feelings of self-reported perceived

control did help performance” (Otten, 2009). Since these results, while interesting, are

based on random individuals, it is not clear if they can be applied to professionals whose

income depends on these moments.

Solomonov, Avugos and Bar-Eli (2015) investigates whether clutch players win games.

While not focusing specifcally on free throws, Solomonov, Avugos and Bar-Eli (2015)

focuses on 16 players deemed to be clutch by NBA “experts”. Solomonov, Avugos and

Bar-Eli (2015) only considers games that were tied, a much more strict defnition of

clutch situations in the point differential sense, but less strict in that they also include

regular season games. The authors conclude that “Top NBA players, like most other

people, do not perform better under pressure situations, at least not while considering

their chances of making a shot, but clutch players do infuence the end-result of the game

in other aspects” (Solomonov, Avugos and Bar-Eli, 2015).

Hickman, Kerr and Metz (2018) investigates how ranking during tournaments effects

the performance of golfers. Golf, like any other sport, exerts pressure on players when

point differential is small. Hickman, Kerr and Metz (2018) fnds that being ranked frst

leads to under performance while being ranked second leads to the highest levels of performance. One would assume that a second ranked player experiences similar pressure to a frst ranked player but the results of that pressure seem vastly different depending on position.

4 Cao, Price and Stone (2011) analyze the effects of pressure on free throw shooting in the NBA. The authors fnd evidence that players generally choke in the clutch, shooting

5-10 percent worse than normal. Cao, Price and Stone (2011) also fnds that, interestingly, chocking is more likely for players who are worse free throw shooters. The paper also fnds that chocking effects losing team greater than winning teams.

Goldman and Rao (2012) analysis pressure in basketball using free throw shooting and offensive rebounding. They also consider whether the game was a home or away game for the shooter. The authors fnd that, as many other papers concluded, free throw shooters do signifcantly worse in clutch situations, with the effect being larger for poor shooters. Interestingly, the paper also fnds that “the home team gets signifcantly better at offensive rebounding in pressure packed moments, while again the road team shows no relationship between performance and pressure”(Goldman and Rao, 2012)

One of the main ways this paper attempts to differentiate itself from others with similar topics is its narrowing of the defnition of clutch. While the narrowing of the defnition (to playoffs and ignoring regular season) should better pinpoint pressure situations, it also has the double-edged sword effect of limiting the data available for analysis.

Focusing strictly on NBA players, while not unique to this paper, also has the added beneft of creating fnancial incentive (and stress) to preform in the clutch.

5 Chapter 2

Data

Spanning the last 22 years, 20 players were chosen as clutch players to be studied. Play- ers were chosen as clutch based on receiving the most amount of votes during that years all-star selection. All star teams are split into 2 sides, east and west and the best players are chosen by the fans and media persons to compete in the all star game which typically takes place in mid February (the mid point of an NBA season). Since many of these players have long tenures as all star leaders, the player with next highest votes was added to this study until the 20th players was reached. Special exceptions were made for players with known clutch reputations that did not ever lead the NBA in votes received during the all star team selection. These exceptions were made for 2 players and strictly based on their reputation and nicknames based on said reputation. Paul Pierce and Damian

Lillard are these players and they regularly make lists on ESPN and Bleacher Report as top clutch players of the NBA in the last 20 years (Favela, 2017).

The clutch data set is available on stats.nba.com. This data set includes last 4- or 5- minute statistics on all players since 1996, this project will use the last 5-minute variant.

Although variables included in this data set range from traditional basketball statistics

6 such as rebounds to advanced statistics such as pace or usage rate, this project will focus on traditional statistics. The main contribution of this data set to this project is clutch time free throw percentage, the dependent variable. Because the clutch free throw data is only available from 1996 to current day, the scope of this project is limited to the most recent two eras of basketball (the post Michael Jordan era and the three-point era).

Clutch players such Michael Jordan, Larry Bird and Magic Johnson are omitted since clutch data is not available for them. While it is possible to include these players using play-by-play data to create clutch data sets, such an undertaking is beyond the scope of this project but would be a worthwhile endeavor for future projects.

2.1 Point Differential and Other Independent Variables

The focus of this paper is to explore if players shoot free throws better or worse when games are close. Secondly, the effect of fatigue will be looked at by looking at minutes played up to clutch time and the effects of rhythm will be looked at using feld goals and free throws taken up to clutch time. The effects of rhythm can be summarized as practice shots taken during the game. For example, if a player has had free throw attempts during the game, he/she has had practice and is therefore in rhythm.

Unfortunately, point differential data is not available in the clutch database and the fnal scores of games are not helpful because these scores are recorded at the end of games and will not tell us anything about pressure during clutch time. Point differential data at the 5-minute mark when clutch time is defned to begin in this paper is needed.

This data was collected manually through basketballreference.com. Scores of games are available with the option of time. If this data was not found on basketball reference.com, data was collected by watching games. Since this paper primarily focuses on playoffs

7 games of the last twenty years, most games were available on YouTube in their entirety or in short formats. Data was collected by watching these games and noting the score at or very near the 5-minute mark and recorded for each game available.

A similar approach was taken towards the collection of the three other independent variables. This paper requires the variables minutes played, feld goals attempted and free throws taken just before clutch time begins, data was collected on the full game statistics and subtracted by the clutch time statistics. For example, If Lebron James played a total of 43 minutes, and according to the clutch data set, four of those minutes are in the clutch, Lebron James must have played 39 minutes before clutch time began. Following this logic, a pre-clutch versions of all three independent variables was created. Figure

2.1 is a simple illustration of the time frame of collected data.

Clut ch Time • Time Independent Variables Dependent Variable Point Differential

Figure 2.1: Time frame of data

8 Chapter 3

Methodology

Since the variable of interest, free throw percentage, is a proportion, a simple regression

(Lm in R) will not be used, instead, a generalized linear model (GLM) with a logit link and the binomial family will be used. This is to insure that our predicted values are also proportions. A detailed discussion of the method used with examples can be found in (Bruin, 2011). This paper will explore free throw attempts, feld goal attempts and minutes played to see what effects these variables have on free throw shooting percentage in the clutch. While point differential captures the mental aspect of free throw shooting, looking at minutes played is an attempt to capture the effect fatigue has on free throw shooting. It is commonly held belief that fatigue at the end games when minutes are high can cause free throw shooters to take shortcuts in their normal routine in order to save energy, causing inconsistency in their form and missing of free throws (Uygur et al.,

2010). Field goal attempts, on the other hand, is meant to capture involvement. Another commonly held belief is that players who are not involved offensively can become “Out of rhythm”. Because these players have not shot the ball much on offense, shooting free throws “cold” can cause them to shoot worse than they normally would.

9 To control for player ability, the model will use a pre-cluch free throw percentage variable (how well do players shoot during the game when it is not clutch time). Lastly, point differential will be checked for symmetry by using the absolute value of the variable. The variables winning and loosing will be created to further explore point differential. Since minute by minute data is not available, the variables winning and loosing will simply refect if the team is winning or loosing at the 5 minute mark.

3.1 Models

Equation 3.1 is a GLM model, with free throw percentage as a proportion during clutch,

all other variables are recorded up to the point of clutch time as described in chapter 2

section 1.

FreeT hrowPercentage = B0 + B1PointD + B2Mnts + B3FGA + B4FTA + B5Control

+B6Winning (3.1) Since point differential (PointD) is the main variable of interest, the frst specifcation of the model will be a simple two variable model which will include the control and point differential. The variables minutes (Mnts), feld goal attempts (FGA), and free throw attempts (FTA) are added one by one in that order. All results will be presented and discussed in the next chapter.

3.2 Player Ranking

While the main aim of this paper is to capture the effects of point differential and other

variables on free throw shooting, if point differential is found to be signifcant by the

model, it would be interesting to rank the players available in the data collected in their

10 clutchness. One way to approach this is to use a simple difference-in-differences comparison to create a ranking of players who perform best in clutch time. Since clutch free throw shooting data is easily available for the entire league for the past 20 years, league averages will be used as the control for our difference-in-difference comparison. An important note here is that the 20 players in this study will not be removed from the league average pool of players. While it would be ideal to remove said players for perfect sta- tistical accuracy, the effect would be small and the effort to remove said players would be large.

11 Chapter 4

Results

Table 4.1 is a summary of the results of the model. Beginning with point differential, its

coeffcient is quite high at nearly .20 and stays consistent within all specifcations of the

model. Point differential is statistically signifcant with a p-values ranging from 0.03 or

0.04. In specifcation 1 of the models, If the average free throw percentage among all player in the data set is used for the control (72%) and point differential is set to 1, the result will be the following.

−3.108 + (5.26 ∗ .72) + .21(1) = .89

Simply put, the average free throw shooter in this data set will shoot around 89% if

point differential equal 1. While this is a nice result, it is important to point out that

these results become unrealistic for point differentials above 2 and higher than 80% free

throw percentage set as control, highlighting some of the shortcomings of this data and

model. Minutes, on the other hand, has a small effect on the model and is insignifcant

with p-values that vary depending on the specifcation. Interestingly, free throw attempts

have a negative coeffcient, suggesting that the theory of rhythm shooters may not be

accurate. Unfortunately, free throw attempts is also insignifcant (a fact that will be

12 discussed later). Field goal attempts, similar to minutes, seems to have a small effect while also being insignifcant. Winning, while having a fairly large coeffcient, is also insignifcant.

Point differential exhibits a strong positive relationship with free throw shooting.

During a tied game, according to this model, the players in the data-set shoot around 69% from the free throw line while an increase in point differential wildly swings percentages.

If their team is ahead just one point, players will shoot 89% and the opposite is true if they are behind. Whether the magnitude of this effect is realistic would require a larger data set with more players and better data. To check if point differential exhibits symmetry, the absolute value of the variable was generated and the same model was ran. This variable was less signifcant than its original counterpart with a p-value of 0.17 compared to 0.04 and its magnitude was similar at 0.19. The following are the results of the model under specifcation 1 if symmetry is imposed on point differential.

−2.87 + (5.57)Control + (.19)PointDi f f erential = FreeT hrowPercentClutch

The variables winning (and loosing) remain insignifcant when using absolute value of point differential but exhibit much lower p-values at 0.12. These results are likely due to less than ideal data, the approach taken in (Hickman, Kerr and Metz, 2018) with minute by minute data would likely produce more elegant results for the variables of winning and loosing. If data were available for each free throw taken, one could see how each free throw is effected by the conditions under which said free throw was taken

(score,time,win/loss). Unfortunately, due to time constraints, the collections of such data is not possible for this paper but would be a worthwhile endeavour for future projects.

13 4.1 Limiting Data To Elimination Games

The intention of this paper is to impose stricter restrictions on clutch situations than its predecessors. Taking this one step further, an even stricter restriction than before will be imposed by only looking at elimination games. The reason this restriction was not implemented for the entire paper and will only be analyzed in this section is limited data.

Imposing such strict limitations on the available data severely limits conclusions that can be drawn from the analysis, but it is nevertheless worth trying. Only specifcation 1 of the model will be looked at, for simplicity.

−2.317 + (3.94)Control + (.25)PointDi f f erential = FreeT hrowPercentClutch

Only point differential is signifcant with a p-value of just over 0.05, its coeffcient increases from 0.20 in the full data set to around 0.25 for the elimination game data set. This suggests that the increased pressure of elimination games may be having an effect on player free throw shooting. Checking for symmetry and adding the variables of winning and loosing produce very insignifcant results with p-values higher than 0.4, these results are likely due to limited data as the sample size has been reduced to below

30 games.

4.2 Free Throw Attempts and Shortcomings of Data

In column 3 of Table 4.1, minutes, free-throw attempts and point differential are all included. Focusing on free throw attempts, the p-value for this coeffcient is 0.15. One of the critical short comings of this data set is that it only includes players whom are considered clutch. These players, in this case, all also happened to be best player or the second-best player on their respective teams. The best players, generally, shoot many

14 Table 4.1: Results

Dependent variable:

Free Throw Percentage

(1) (2) (3) (4) (5)

Point Differential 0.211∗∗ 0.212∗∗ 0.213∗∗ 0.195∗ 0.196

(0.102) (0.102) (0.103) (0.150) (0.152)

Control 5.263∗∗ 4.996∗ 5.200∗ 5.235∗ 5.167

(2.293) (2.597) (3.034) (3.045) (3.184)

Free Throw Attempts −0.029 −0.019 −0.019 −0.021

(0.136) (0.156) (0.156) (0.159)

Minutes −0.011 −0.013 −0.017

(0.082) (0.083) (0.101)

Winning 0.147 0.140

(0.860) (0.867)

Constant −3.108∗ −2.706 −2.535 −2.558 −2.490

(1.647) (2.480) (2.799) (2.800) (2.946)

Note: ∗ p<0.1; ∗∗ p<0.05

15 free throws during the game and therefore do not lack “practice” free throws before they enter clutch time. Role players (defned in this paper to be non-allstar players who start for their respective teams) are more likely to lack free throw attempts during the game and they are not included in this data set. If this data set were expanded to include these players, it is likely that this variable could change drastically in its magnitude and signifcance. A league wide study of this variable could produce better results and shed light on whether having shot free throws in the game (being involved) could have a positive impact on free throw shooting in the clutch. As it stands in this paper, free throw shooting may be capturing fatigue instead of rhythm as intended. Since clutch players take many free throws during the game, this could have the opposite effect of rhythm and cause tired legs, explaining the negative coeffcient observed.

4.3 Player Ranking

As outlined in chapter three, a difference-in-differences comparison is made to create a ranking of least to most clutch of the players available in the data set. This section will be comparing the differences in free throw % in and out of clutch for league averages to the same differences for the 20 players. The control group is the rest of the leagues players for the past 20 years. During the regular season, from 1999 to 2018 all player in the NBA shot 75.62% from the free throw line. In the clutch, these same players shot

70.1% from the free throw line. The two tailed P-value for this comparison is less than

0.0001. The results of the difference-in-differences comparison are presented in Table

4.2 below.

16 Table 4.2: Player Ranking

Rank Player FT-Diff-Diff Rank Player FT-Diff-Diff

1 Damian Lillard +16.62 11 Ray Allen +6.33

2 Russell Westbrook +14.7 12 Kobe Bryant +4.57

3 Dwight Howard +12.68 13 Chris Paul +4.37

4 James Harden +11.87 14 Shaquille O’neal +3.07

5 Stephan Curry +9.82 15 Kevin Garnett +2.72

6 Dwayne Wade +9.75 16 Tim Duncan +2.06

7 Lebron James +8.34 17 Kevin Durant +1.83

8 Dirk Nowitzki +8.27 18 Carmelo Anthony -0.08

9 Clay Thompson +8.22 19 Steve Nash -0.64

10 Allen Iverson +7.36 20 Paul Pierce -2.48

Looking at the results, it appears that the all star voting outcomes do an effective job of selecting clutch players. Most of the players in this study performed better than the league average control group, there are some notable exceptions and unexpected outcomes worth pointing out. Damian Lillard, who, as discussed in the introduction has earned the nickname “Dame Time” for his late game heroics seems to perform according to that reputation. Out of the 20 players, Damian fnished frst above many of the greatest basketball players in the history of the NBA. More surprising than Damian was Dwight

Howard, who fnished third overall. Dwight Howard, over the course of his career, was consistently one of the worst free throw shooters in the league shooting just over 56% from the free throw line. However, he improved his free throw shooting greatly in the clutch. Player with clutch reputations such Kobe Bryant, Dirk Nowitzki, Allen Iverson and Stephan Curry performed as expected, improving their free throw shooting in the

17 clutch. On the other side of the spectrum, Paul Pierce whose reputation for clutchness earned him the nickname “The Truth” performed the worst in this study, fnishing 2.45 points below league average. Steve Nash, one of the best free throw shooters in the history of the NBA, also came in second to last.

While it is interesting to look at how these players improved or did worse than their own averages in the clutch, it is important to keep in mind that this list simply attempts to look at how clutch moments effect free throw shooting psychologically and should not be used as a guide to pick whom should shoot free throws if one were given the choice between these players. Steve Nash is a great example of this, he shot 90.4% from the free throw line during his career giving him little room to improve in the clutch. In the clutch, he still shot 84 percent from the free throw. Dwight Howard, whos ranked much higher than Steve Nash on this list, shot 57% from the free throw line during his career and improved to 64% in the clutch. While Dwight showed impressive improvements, one would still want Steve Nash to shoot free throws at the end of games.

18 Chapter 5

Conclusion

This paper investigates what affects free throw shooting in the clutch. While point differential was the main focus, free throw attempts, and minutes were also considered as possible candidates for potential variables that may effect how players perform at the free throw line. While minutes and free throw shooting were insignifcant in the model, it was concluded that with a better, larger data set that incorporates more players, specifcally role player and not just stars, these variables may become signifcant. Anecdotal evidence suggests that role players are more likely to suffer from the ill effects of not taking enough free throws during the course of the game, causing uncharacteristic mistakes due to being “out of rhythm” once clutch time beings. Furthermore, the surprising negative coeffcient of free throw attempts points to a possible fatigue aspect of free throw shooting where a large number of free throws taken may cause tired legs and more misses, an interesting aspect of free throw shooting that can be looked at in future papers. Point differentials signifcance in the model signals that there may be something to the psychological aspect of free throw shooting as described in (Otten, 2009), even in NBA players and not just armatures as studied in (Otten, 2009).

19 Lastly, using a difference-in-difference method, a ranking of players in the data set was created to see who handled the pressure of the moment best, using league averages as the control group. Surprising results such as Dwight Howard ranking third overall and

Steve Nash ranking nineteenth overall were uncovered, while player like Damian Lillard proved that their clutch reputation was well earned. Unsurprisingly, most of these players with clutch reputations proved to be clutch.

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